Continuity mistake: As Shirley Jones is singing "In love with Me" at one point, she's sitting down, and is slouching back. The shot changes to the side, and she's sitting up straight, and is much higher against the counter than she was. Her hands have changed position as well, she's no longer holding onto the cup she had in her left hand. (01:19:55)
Revealing mistake: At a certain point we see the arid, dry Santa Monica Mountains of Los Angeles in the upper left of the picture with a huge high-tension electrical tower at the summit. The film is set in 1912 in Iowa, a green, rainy state which is also completely flat, with no mountains. Then again, we see the arid, dry Santa Monica Mountains in the upper right. (00:08:27)
Continuity mistake: In the beginning when the Anvil Salesman gets on the train, he sits down, arms to the side, the camera angle changes, and his arms are immediately on his hat adjusting it. (00:03:10)
Visible crew/equipment: During the song "Wells Fargo Wagon" film equipment and lights can be seen reflected in the store windows.
Revealing mistake: During "Marian the Librarian," Marian is seen doing a little dance on the table before being hushed by the people in the library. Like the incident with Winthrop in "Gary, Indiana," you can see that she did not actually do this dance. Tap sounds were added in later to make it seem like she did.
Revealing mistake: At the end of Winthrop's version of "Gary, Indiana," we see what appears to be a little tap dance done by Winthrop that concludes the song. Upon close observation, however, you can tell that Winthrop does not actually do this dance. He just twirls around and tap noises are added in to make it seem like he is tapping.
Other mistake: During the scene where the teens are performing that "kicking" routine in the gymnasium as led by Tommy Djilas, you can see Harold Hill in the back left of the screen, watching. Right before the number ends, a costume prop can be seen coming from the back middle of the dancers and hitting Robert Preston in the face.
Factual error: Professor Harold Hill asks the mothers of River City about their sons, "Is he starting to memorize jokes from 'Captain Billy's Whiz Bang?'" While the film is set in 1912, the first issue of the pulp magazine, "Captain Billy's Whiz Bang," did not appear until 1919. "Whiz Bang" was a term coined by soldiers in World War I (commencing in 1914), which referred to a rocket that "whizzed" by and exploded with a "bang." (00:20:00)
Continuity mistake: After "'Till There Was You," Harold and Marian kiss. A shot of their reflections in the river shows this happening, and then it shows their heads part. When the shot changes to a close up of them they are kissing again.
Audio problem: If you listen carefully during the conversation between Marian and Ameryllis before "Goodnight, My Someone," you may notice something quite strange. After she is comforted by Marian, Ameryllis asks her, "If A GIRL doesn't have a sweetheart, who's HE going to say goodnight to on the evening star?"
Audio problem: During the first scene where the traveling salesmen are on the train, one of the characters says "He don't know one note from another". You can then hear a woman's voice laughing, even though there are only men on the train.
Factual error: At the start of the movie, the train the salesmen are on travels from Brighton, Illinois to River City, Iowa. The entire time we see, through the car windows, lush, green farmland. The problem is, to get from Illinois to Iowa, one must cross the Mississippi River, which is over a mile wide, but there is never any sign of either a river or a railroad bridge.
Other mistake: Immediately after the unexpected breakup of the 4th of July festivities at the High School, Professor Hill intercepts Zaneeta on her way to the "library." 4th of July is a national holiday and it is unlikely the library would be open since it is a public facility ("he left the city the library building, but he left all the books to her"). Second, even if the library was open, this scene is less than five minutes after the festivities were unexpectedly broken up, so Marian (the librarian) would not have scheduled an opening time until later, after the festivities were expected to end.
Character mistake: When Marian is correcting Amaryllis for the girls' poor grammar in saying "can I" instead of "may I" over the cross-hand piece, the girl then asks if she can go play that cross-hand piece and Marian replies, "now you can play your cross-hand piece."
Revealing mistake: During the July 4th festivities at Madison Park, Professor Harold Hill prompts four school board members (the Buffalo Bills quartet) into performing the song "Sincere," allowing Hill to slip away into the crowd. As they complete the last verse, the singers stroll into a wide shot with a fireworks display in the background. However, the skybursts are oddly magnified and erratically shift positions against the background, revealing that the fireworks display is a large but clumsily-edited rear-screen projection.
Revealing mistake: As the passengers are getting on the train at the start, their shadows reveal that the train car wheels and springs are painted on a flat surface. (00:00:10)
Factual error: A poster promoting the July 4th fireworks spectacle includes an illustration of two American flags - each with 50 stars, rather than the 48 stars which they should have at the time. (00:46:40)
Continuity mistake: Mayor Shinn thanks the crowd for attending the Fourth of July exercises indoors at the gymnasium due to "the weather being so chancy" (meaning a good probability of rain). Mayor Shinn adds that the July 4th fireworks display will be held that evening unless the rain prohibits it. However, the year is 1912, and no advanced weather-tracking technology exists; so, they have no way of predicting the weather except by direct observation. Therefore, the mayor must be basing his cautionary weather statements on direct observation of overcast and stormy conditions. But, when Professor Harold Hill works the crowd into an excited frenzy that bursts out of the gymnasium and into the streets, it is revealed that the sky is perfectly clear and blue, with the sun shining brightly. There is no indication of inclement weather whatsoever. In fact, it remains clear and never rains in River City throughout the course of the entire movie.
Answer: The movie doesn't take place in Indiana. It takes place in River City, Iowa, which is established multiple times throughout the movie.